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Chin. Phys. B, 2014, Vol. 23(7): 070507    DOI: 10.1088/1674-1056/23/7/070507
Special Issue: TOPICAL REVIEW — Statistical Physics and Complex Systems
TOPICAL REVIEW—Statistical Physics and Complex Systems Prev   Next  

Level spacing statistics for two-dimensional massless Dirac billiards

Huang Lianga b, Xu Hong-Yaa b, Lai Ying-Chengb c d, Celso Grebogid
a Institute of Computational Physics and Complex Systems and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou 730000, China;
b School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA;
c Department of Physics, Arizona State University, Tempe, AZ 85287, USA;
d Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences, King's College, University of Aberdeen, UK
Abstract  Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The searching for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation (orWeyl equation) and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different, rendering distinct level spacing statistics.
Keywords:  quantum chaos      level spacing statistics      Dirac billiards      graphene billiards  
Received:  05 March 2014      Revised:  22 May 2014      Published:  15 July 2014
PACS:  05.45.Mt (Quantum chaos; semiclassical methods)  
  03.65.Pm (Relativistic wave equations)  
  73.22.Dj (Single particle states)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11005053, 11135001, and 11375074), the Air Force Office of Scientific Research (Grant No. FA9550-12-1-0095), and the Office of Naval Research (Grant No. N00014-08-1-0627).
Corresponding Authors:  Huang Liang     E-mail:  huangl@lzu.edu.cn
About author:  05.45.Mt; 03.65.Pm; 73.22.Dj

Cite this article: 

Huang Liang, Xu Hong-Ya, Lai Ying-Cheng, Celso Grebogi Level spacing statistics for two-dimensional massless Dirac billiards 2014 Chin. Phys. B 23 070507

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